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He may go next month – and reports suggest Manchester City believe they can strike a deal for the Chilean – or he will walk away from the Emirates next summer for nothing.
So it's time for Arsenal and Arsène Wenger to get thinking; how can they replace the club's most important and undoubtedly best player? The answer is certainly not a simple one.
When a player of Sánchez's quality departs, the gap that is left is almost impossible to fill. Last season he was outstanding, contributing to 49 goals in 51 appearances for the Gunners.
But it was still not enough to secure Arsenal a place in the Premier League's top four, which is why Sánchez has decided he wants out. The inconsistent Mesut Özil may follow, but replacing the German should be an easier task than finding someone to fill Sánchez's boots.
Wenger needs to go old school. There was a time when the Frenchman would sell off a prized asset – think Nicolas Anelka – only to replace him with someone better, like Thierry Henry.
Wenger needs to find a diamond in the rough. And this week reports have emerged the Gunners have been watching PSV winger Hirving Lozano and may make a move for the Mexican in January.
But is he ready for the Premier League and, more specifically, a club with ambitions of returning to the Champions League? We've run the rule over the 22-year-old to see if he can be the long-term replacement for Sánchez at Arsenal.
Who is Hirving ‘Chucky' Lozano?
Nicknames can often tell you a lot about a footballer. Alessandro Del Piero was Pinturicchio, ‘The Little Painter'. Javier Zanetti, ‘El Tractor‘. While Leo Messi is affectionally known as La Pulga, ‘The Flea'.
But Lozano was given his nickname, Chucky, for a very different reason. The story goes that as a youth player at Pachuca, his first club, the winger would hide under his team-mates' beds on away trips before jumping out and scaring them.
For doing so he was compared to the facially scarred, orange-haired serial killer doll from from the Child's Play films. And so ‘El Chucky' was born.
It wouldn't be long, though, until he was terrorising opposition defences. He made his Liga MX debut for Pachuca on February 8, 2014, against Club America. He was introduced from the substitutes' bench in the 83rd minute and five minutes later, made an immediate impact.
Lozano received a pass on the right flank, just inside his on half. There were no nerves and he drove straight at the America defence, who backed off. The winger advanced to the edge of the penalty area, shifted the ball onto his left foot and drilled a shot into the bottom corner. It was some introduction.
He would make 15 further appearances during the 2013/14 season and ended the campaign with two goals and four assists. His star was on the rise and over the next three seasons Lozano went from strength to strength.
The 2014/15 season resulted in nine goals and seven assists, while 2015/16 saw the winger, deployed on the left flank, strike 12 times and lay on ten goals for his team-mates.
And, during the 2016/17 season Lozano netted 18 goals in addition to claiming seven assists as Pachuca won the Liga MX and CONCACAF Champions League titles.
His form, unsurprisingly, earned admiring glances from Europe's elite. Manchester United and Manchester City were reportedly interested, with the latter considering a move. But PSV Eindhoven got their first and Lozano signed a six-year deal with the club in June.
“Hirving is a different kind of player, he's a player with great individual quality who makes a lot of difference on the field,” Pachuca's goalkeeper Oscar Perez said before his team-mate departed.
“Hopefully he's able to sort things out the best way possible and be able to stay happy and keep developing and becoming known. I really value him and wish him the best and all the success in the world.”
Having come over from Mexico, Lozano would've been forgiven if he was to make a slow start in Dutch football. Instead, the opposite occurred. He netted 31 minutes into his Eredivisie debut and has scored six goals in six league outings.
Arsenal scout Steve Rowley has been over to Holland to watch the winger and clearly likes what he has seen. Which is why Arsenal are now weighing up a move.
What would Lozano bring to Arsenal?
If Arsenal were to pursue a deal for Lozano in January, and Sánchez was to move on for pastures new, then the Gunners would be signing a player with similar characteristics to the Chilean.
Lozano has spent the majority of his formative years being used out wide, much like Sánchez was at Udinese. From this position on the left flank, he often cuts inside onto his stronger right foot to link play or have a shot on goal. Sound familiar?
His first goal for PSV highlighted the quality Lozano has with the ball at his feet. In the first still below, he has gathered possession out on the wing before moving into the penalty area.
He slows down the AZ centre-back expertly before shifting the ball onto his right foot. And with a clear sight of goal, Lozano drills a shot into the near post which wrong foots the goalkeeper.
But that goal was far from a one off. When he gets the ball in the final third Lozano is fast and direct, and the stats back that up.
In his six league appearances for PSV, he is averaging 2.2 dribbles per game and 3.8 shots on goal. They are impressive figures for a player still feeling his way into a new team and a new style of football.
By comparison, Sánchez last season averaged 3.4 shots and 2.9 dribbles per game in the Premier League. So the numbers are not dramatically different but the quality between the two divisions certainly is, and that must be taken into account.
But clearly Sánchez and Lozano are two players cut from the same cloth. The major difference is the former is a 28-year-old who has honed his craft to become one of the world's best, while the other is still improving and learning the game.
So if Lozano does join Arsenal in January, and Sánchez does move on, it would be wrong to expect the young Mexican to be an instant replacement.
However, with the right guiding hand, El Chucky has the potential to be a leading man. And one Arsenal should ensure they don't miss out on.